To find the linear equation given the slope and a point, we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is the point, and \( m \) is the slope. Here, we have:
- \( m = -4 \)
- \( P = (-3, 5) \) which gives \( x_1 = -3 \) and \( y_1 = 5 \)
Substituting these values into the point-slope form:
\[ y - 5 = -4(x - (-3)) \]
This simplifies to:
\[ y - 5 = -4(x + 3) \]
Now, we can distribute the -4:
\[ y - 5 = -4x - 12 \]
Next, we add 5 to both sides to solve for \( y \):
\[ y = -4x - 12 + 5 \]
\[ y = -4x - 7 \]
Thus, the linear equation is:
\[ \boxed{y = -4x - 7} \]